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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Apply nat_ind with λ x1 . SNo (exp_SNo_nat x0 x1) leaving 2 subgoals.
Apply exp_SNo_nat_0 with x0, λ x1 x2 . SNo x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_1.
Let x1 of type ι be given.
Assume H1: nat_p x1.
Assume H2: SNo (exp_SNo_nat x0 x1).
Apply exp_SNo_nat_S with x0, x1, λ x2 x3 . SNo x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_mul_SNo with x0, exp_SNo_nat x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.